1. Field of Invention
The present invention relates generally to machine vision, and more particularly, to a method of modeling the shadows cast by various features of an object onto its own surface under certain lighting conditions, to allow a machine to recognize the image of that object when illuminated by a wide variety of lighting conditions.
2. Description of Related Art
It is clear that changes in lighting can have a large effect on how an object, such as a person, looks. Understanding this is essential to building effective object recognition systems.
U.S. patent application Ser. No. 09/705,507, filed 3 Nov. 2000, entitled “Lambertian Reflectance and Linear Subspaces”, the disclosure of which is hereby incorporated by reference, considered the relationship between the function that describes the lighting intensity, and the reflectance function that describes how much light an object reflects as a function of its surface normal, under a given lighting condition. Representing these functions as spherical harmonics, it was shown that for Lambertian reflectance the mapping from lighting to reflectance is a convolution with a nearly perfect low-pass filter. High-frequency components of the lighting hardly affect the reflectance function. Therefore, nearly all Lambertian reflectance functions could be modeled as some linear combination of nine spherical harmonic components.
These low-dimensional approximations have two key advantages. First, they are described with few parameters, thus optimization is simpler. Moreover, the images produced under low-frequency lighting are inherently immune to small changes in orientation. A small rotation in the surface normal is equivalent to a small rotation in the light. However, low-frequency light does not appreciably change with a small rotation. The analysis shows this, in that an image produced by an nth order harmonic light component is computed by taking an nth degree polynomial of the components of the surface normal.
U.S. patent application Ser. No. 09/967,206, incorporated by reference above, expanded the spherical harmonic approach to consider both the effects of broadened specular reflection as well as Lambertian reflection. Thus, the reflectance function that describes how much light an object reflects as a function of its surface normal, under a given lighting condition was made more realistic.
That work has considered the effects of attached shadows, which arise locally, when some portion of the object is facing away from the light. However, it has not addressed the problems that arise when one part of an object casts a shadow on a different part of the object. This is important, because many objects of interest are characterized by features whose prominence produces cast shadows over a significant portion of the surrounding surface, especially at low angles of illumination (high angles of incidence relative to the surface normal). Indeed, no natural object is convex, and relatively few manufactured objects are, and even fewer when seen in combination. Thus, cast shadows can be expected to play an important role in reflection, and, therefore must be included in harmonic treatments.